My Learning Cart

What is the space complexity of DFS using a recursive approach?

Practice Questions

Q1
What is the space complexity of DFS using a recursive approach?
  1. O(V)
  2. O(E)
  3. O(V + E)
  4. O(1)

Questions & Step-by-Step Solutions

What is the space complexity of DFS using a recursive approach?
  • Step 1: Understand what DFS (Depth-First Search) is. It is a method for exploring nodes and edges of a graph or tree.
  • Step 2: Recognize that DFS can be implemented using recursion, which means the function calls itself to explore deeper into the graph.
  • Step 3: When a function is called in recursion, it uses a part of the computer's memory called the call stack.
  • Step 4: Each time the DFS function calls itself, a new layer is added to the call stack.
  • Step 5: The maximum depth of the call stack corresponds to the maximum number of nodes that can be on the stack at one time.
  • Step 6: In the worst case, the maximum depth of the call stack is equal to the number of vertices (V) in the graph.
  • Step 7: Therefore, the space used by the call stack in the recursive DFS is proportional to the number of vertices.
  • Step 8: This leads us to conclude that the space complexity of DFS using a recursive approach is O(V).
No concepts available.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely